Answer:
Explanation:
Remark
First take a look at A. It is a pretty good idea always to write the formula you are using before you begin a solution and go step by step from the formula. Also write your givens. I know it sounds like a lot of work. It really isn't. You are creating a habit.
Givens
n = 8
Sn = ?
d = -6
a = 90
Formula
S8 = a + (n - 1)*d
Solution
s8 = 90 + (8-1)*-6
s8 = 90 + 7 * -6
S8 = 80 - 42
S8 = 38
Part B
Here's where the formula is your friend. Let's suppose it is. Then solve for n. If we get an integer for the term number, then all is well. If we don't, and we get some kind of fraction, then 5 is not a member of the sequence.
Givens
Sn = 5
n = ?
d = -6
Formula
Sn = a + (n - 1)*d
Solution
5 = 90 + (n - 1)*-6 Subtract 90 from sides
5-90 =90-90 +(n - 1)*-6 Combine
-85 = (n -1)*-6 Divide by - 6
-85/-6 = (n - 1)-6/-6
14 1/6 = n - 1 Add 1 to both sides
14 1/6 +1 = n - 1 + 1 Combine
15 1/6 = n
But a fraction is not permitted. So 5 is not a member of the sequence